# Tag Info

This can take exponentially many steps, as Laakeri explained. You can build a system that cycles with period $p$. In particular, the update rule is $x_i = x_{i-1 \bmod p}$ for all $i$, with variables $x_0,\dots,x_{p-1}$. Let $p_1,\dots,p_k$ be the first $k$ primes. Concatenate $k$ disjoint systems, each of which cycles with period $p_i$. Then the period ...